Collapse Rate of Solutions of the Cauchy Problem for the Nonlinear Schrödinger Equation

We prove that solutions of the Cauchy problem for the nonlinear Schrödinger equation with certain initial data collapse in a finite time, whose exact value we estimate from above. We obtain an estimate from below for the solution collapse rate in certain norms.

     

On the Fredholm radius of integral operators of potential theory

The Fredholm radius of the integral operators of the theory of n-dimensional harmonic potentials on surfaces with edges, acting in certain weighted Hölder type spaces, is found. Results for integral operators are derived from theorems on operators in certain auxiliary contact problems.Translated from Problemy Matematicheskogo Analiza, No. 11, pp. 109–133, 1990.     

Colorings of k-balanced matrices and integer decomposition property of related polyhedra

We show that a class of polyhedra, arising from certain 0,1 matrices introduced by Truemper and Chandrasekaran, has the integer decomposition property. This is accomplished by proving certain coloring properties of these matrices.     

Performance analysis of an irreversible Miller cycle with considerations of relative air–fuel ratio and stroke length

The performance of an air standard Miller cycle is analyzed using finite-time thermodynamics. The results show that if compression ratio exceeds certain value, the power output first increases and then starts to decrease with increasing relative air–fuel ratio, while if compression ratio exceeds certain value, the power output decreases with increasing relative air–fuel ratio. The results also show that if compression ratio is less than certain value, the power output decreases with increasing stroke length, while if compression ratio exceeds certain value, the power output first increases and then starts to decrease with increasing stroke length. With further increase in compression ratio, the increase of stroke length results in decreasing the power output. The results obtained from this work can be helpful in the design and evaluation of practical Miller engines.     

A three-dimensional inverse problem of determination of the unknown coefficient in a boundary condition of the third kind

One proves an existence and uniqueness theorem in the small and a uniqueness theorem in the large for the inverse problem of determination of the unknown coefficient in a certain boundary condition from certain information about Green's function of the direct problem.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 128, pp. 102–104, 1983.     

An oscillating operator related to wave equations in the block spaces

In this article, we study certain oscillating multipliers related to Cauchy problem for the wave equations on the Euclidean space and on the torus. We obtain that, at the end point, these operators are bounded from the L _p spaces to certain block spaces.     

Nonsteady deformation of SKN-18 rubber

In certain polymers, in certain conditions of temperature and deformation, orientation processes predominate over processes of thixotropic structural breakdown.Scientific-Research Institute of Rubber and Latex Goods, Moscow. V. I. Lenin Moscow State Pedagogical Institute. Translated from Mekhanika Polimerov, No. 2, pp. 350–351, March–April, 1974.     

Elementary estimates for a certain typeof Soto-Andrade sum

This paper shows that a certain type of Soto-Andrade sum can be estimated in an elementary way which does not use the Riemann hypothesis for curves over finite fields and which slightly sharpens previous estimates for this type of Soto-Andrade sum. As an application, we discuss how this implies that certain graphs arising from finite upper half planes in odd characteristic are Ramanujan without using the Riemann hypothesis.

     

On Parabolic Cylinder Functions

In this paper certain properties of the parabolic cylinder functionsas formulated by Wells & Spence (1945) are discussed. Theparticular features studied are certain orthogonality propertiesand the character of the cigenvalues when the parabolic cylinderfunctions are considered as arising from essentially two-parametereigenvalue problems.     

A construction of rational elliptic surfaces with the non-surjective boundary map on K 2

We present some rational elliptic surfaces over a certain field such that certain open subschemes do not satisfy the surjectivity of the boundary map on K ₂ arising from the localization sequence. We consider two cases that the base field is transcendental over its prime subfield and that the base field is characteristic zero.     

Triangle Buildings and Actions of Type III1/q

We study certain group actions on triangle buildings and their boundaries and some von Neumann algebras which can be constructed from them. In particular, for buildings of orderq?3 certain natural actions on the boundary are hyperfinite of type III_1/q².     

A Generalization of the Hilbert Basis Theorem

A generalization of the Hilbert basis theorem in the geometric setting is proposed. It asserts that, for any well-describable (in a certain sense) family of polynomials, there exists a number C such that if P is an everywhere dense (in a certain sense) subfamily of this family, a is an arbitrary point, and the first C polynomials in any sequence from P vanish at the point a, then all polynomials from P vanish at a.     

Primitive cohomology and the tube mapping

Let X be a smooth complex projective variety of dimension d. We show that its primitive cohomology in degree d is generated by certain “tube classes,” constructed from the monodromy in the family of all hyperplane sections of X. The proof makes use of a result about the group cohomology of certain representations that may be of independent interest.     

A generalization of a minimax theorem of Fan via a theorem of the alternative

A minimization problem for a functional on a convex subsetC of a normed linear space is considered. Under certain hypotheses, optimality in a certain subset ofC implies the validity of first-order necessary optimality conditions for the problem inC. The result is applied to a problem in optimal periodic control of neutral functional differential equations.This work was partially supported by a grant from Deutsche Forschungsgemeinschaft and by AFOSR under Grant No. AFOSR-84-0398.     

Weak bases and quasi-pseudo-metrization of bispaces

In this paper it is obtained a quasi-pseudo-metrization theorem which provides a certain unification in the treatment of the biquasi-metrization problem when it is considered via sequences of neighborhoods of each point satisfying certain properties. In particular, the well-known theorems of Fox, Raghavan, Künzi, and Raghavan and Reilly are deduced from our results. We also obtain some quasi-metrization theorems in terms of pairwise locally symmetric bifunctions.     

Single polynomials that correspond to pairs of cyclotomic polynomials with interlacing zeros

We give a complete classification of all pairs of cyclotomic polynomials whose zeros interlace on the unit circle, making explicit a result essentially contained in work of Beukers and Heckman. We show that each such pair corresponds to a single polynomial from a certain special class of integer polynomials, the 2-reciprocal discbionic polynomials. We also show that each such pair also corresponds (in four different ways) to a single Pisot polynomial from a certain restricted class, the cyclogenic Pisot polynomials. We investigate properties of this class of Pisot polynomials.     

Continuity properties of majority rule with intermediate preferences

This paper shows that certain conditions which have previously been shown (by Grandmont) to be sufficient for a society's majority rule relation to be transitive or acyclic are also sufficient for the map from distributions of voter preferences to indices identified with their majority rule relations to be continuous. Applications of this result to societies with certain classical assumptions on preferences reveal that, in such societies, the map from distributions of voter preferences to their majority rule equilibria is also continuous.     

Reconstruction of the medium by iterative-asymptotic method

Interpretation of geoelectric fields gives rise to multidimensional inverse problems, which include many problems for quasi-layered media. Such problems are solved by an iterative-asymptotic method. In the present article we consider a particular implementation of the method designed for a certain model of the medium, a certain method of solving the one-dimensional inverse problem, and a certain representation of magnetotelluric sounding data. Translated from Prikladnaya Matematika i Informatika, No. 2, pp. 44–55, 1999.     

Combined branch-and-bound and cutting plane methods for solving a class of nonlinear programming problems

We propose unified branch-and-bound and cutting plane algorithms for global minimization of a functionf(x, y) over a certain closed set. By formulating the problem in terms of two groups of variables and two groups of constraints we obtain new relaxation bounding and adaptive branching operations. The branching operation takes place in y-space only and uses the iteration points obtained through the bounding operation. The cutting is performed in parallel with the branch-and-bound procedure. The method can be applied implementably for a certain class of nonconvex programming problems.On leave from Institute of Mathematics, Hanoi, by a grant from Alexander-von-Humboldt-Stiftung.